Geodesic
Regularity and uniqueness of the solution of the control problem for the stationary equations of magnetic hydrodynamics with mixed boundary conditions
Dalʹnevostočnyj matematičeskij žurnal, Tome 4 (2003) no. 2, pp. 264-275.

Voir la notice de l'article provenant de la source Math-Net.Ru

The control problems for the stationary equations of viscous magnetic hydrodynamics under mixed boundary conditions for the velocity and electric and magnetic fields are considered. The regularity of the Lagrange multiplier for the considered control problems is proved. The sufficient conditions of uniqueness of solutions of the control problem for the specific cost functional are established. 
@article{DVMG_2003_4_2_a8,
     author = {R. V. Brizitskii},
     title = {Regularity and uniqueness of the solution of the control problem for the stationary equations of magnetic hydrodynamics with mixed boundary conditions},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {264--275},
     publisher = {mathdoc},
     volume = {4},
     number = {2},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2003_4_2_a8/}
}
TY  - JOUR
AU  - R. V. Brizitskii
TI  - Regularity and uniqueness of the solution of the control problem for the stationary equations of magnetic hydrodynamics with mixed boundary conditions
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2003
SP  - 264
EP  - 275
VL  - 4
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2003_4_2_a8/
LA  - ru
ID  - DVMG_2003_4_2_a8
ER  - 
%0 Journal Article
%A R. V. Brizitskii
%T Regularity and uniqueness of the solution of the control problem for the stationary equations of magnetic hydrodynamics with mixed boundary conditions
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2003
%P 264-275
%V 4
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2003_4_2_a8/
%G ru
%F DVMG_2003_4_2_a8
R. V. Brizitskii. Regularity and uniqueness of the solution of the control problem for the stationary equations of magnetic hydrodynamics with mixed boundary conditions. Dalʹnevostočnyj matematičeskij žurnal, Tome 4 (2003) no. 2, pp. 264-275. http://geodesic.mathdoc.fr/item/DVMG_2003_4_2_a8/

[1] G. V. Alekseev, Teoreticheskii analiz obratnykh ekstremalnykh zadach dlya statsionarnykh uravnenii magnitnoi gidrodinamiki vyazkoi neszhimaemoi zhidkosti, Preprint No 1 IPM DVO RAN, Dalnauka, Vladivostok, 2002, 78 pp.

[2] G. V. Alekseev, R. V. Brizitskii, “Razreshimost obratnykh ekstremalnykh zadach dlya statsionarnykh uravnenii magnitnoi gidrodinamiki vyazkoi zhidkosti so smeshannymi granichnymi usloviyami”, Dalnevost. mat. zh., 4:1 (2003), 108–126

[3] A. Valli, Orthogonal decompositions of ${\mathbf L}^2(\Omega)^3$, Preprint UTM 493. Department of Mathematics, Galamen, University of Toronto, 1995

[4] A. Alonso and A. Valli, “Some remarks on the characterization of the space of tangential traces of ${\mathbf H}(rot;\Omega)$ and the construction of the extension operator”, Manuscr. Math., 89 (1996), 159–178 | DOI | MR | Zbl

[5] L. Hou, S. Ravindran, “Computations of boundary optimal control problems for an electrically conducting fluid”, J. Comp. Phys., 128 (1996), 319–330 | DOI | MR | Zbl

[6] G. V. Alekseev, “Razreshimost statsionarnykh zadach granichnogo upravleniya dlya uravnenii teplovoi konvektsii”, Sib. mat. zhurn., 39:5 (1998), 982–998 | MR | Zbl

[7] G. V. Alekseev, “Razreshimost obratnykh ekstremalnykh zadach dlya statsionarnykh uravnenii teplomassoperenosa”, Sib. mat. zhurn., 42:5 (2001), 971–991 | MR | Zbl

[8] G. V. Alekseev, “Obratnye ekstremalnye zadachi dlya statsionarnykh uravnenii teorii massoperenosa”, Zh. vychisl. matem. i matem. fiz., 42:3 (2002), 380–394 | MR | Zbl

[9] A. D. Ioffe, V. M. Tikhomirov, Teoriya ekstremalnykh zadach, Nauka, M. | MR

[10] G. V. Alekseev, A. B. Smyshlyaev, D. A. Tereshko, Neodnorodnye kraevye zadachi dlya statsionarnykh uravnenii teplomassoperenosa, Preprint No 19 IPM DVO RAN, Dalnauka, Vladivostok, 2000, 60 pp.